In short: Optics (Ray + Wave) is the second highest-weightage unit in CBSE Class 12 Physics, carrying 14 marks out of 70. It covers reflection, refraction, lenses, prisms, total internal reflection, optical instruments in Ray Optics, and interference, diffraction, polarization in Wave Optics. Expect 1-2 derivations and 2-3 numericals every year. Nail this unit and you lock in 20% of your Physics paper.
Unit Overview and Marks Distribution
| Chapter | Key Topics | Expected Marks |
|---|---|---|
| Ch 9: Ray Optics and Optical Instruments | Mirror/Lens formula, Prism, TIR, Microscope, Telescope | 8-9 |
| Ch 10: Wave Optics | Young's Double Slit, Diffraction, Polarization | 5-6 |
| Total | 14 |
For the complete chapter-wise breakdown across all units, check the CBSE Class 12 Physics marks weightage.
Ray Optics: Key Formulas
Mirror Formula and Magnification
Mirror formula: 1/v + 1/u = 1/f
Magnification: m = -v/u = h'/h
Sign convention (New Cartesian):
- All distances measured from the pole
- Direction of incident light is positive (+ve x-axis)
- Object distance (u) is always negative for real objects
- Focal length: negative for concave, positive for convex
Lens Formula and Power
Thin lens formula: 1/v - 1/u = 1/f
Power of a lens: P = 1/f (in metres) → unit is Dioptre (D)
Lens maker's formula: 1/f = (n₂/n₁ - 1)(1/R₁ - 1/R₂)
Where n₂ = refractive index of lens, n₁ = refractive index of medium.
Combination of thin lenses in contact:
- P = P₁ + P₂ + P₃
- 1/f = 1/f₁ + 1/f₂ + 1/f₃
Refraction Through a Prism
Prism formula: n = sin[(A + δₘ)/2] / sin(A/2)
Where A = angle of prism, δₘ = angle of minimum deviation.
At minimum deviation:
- r₁ = r₂ = A/2
- i₁ = i₂ = (A + δₘ)/2
- The refracted ray inside the prism is parallel to the base
Dispersion: Different wavelengths refract at different angles. Violet deviates most, red deviates least.
Total Internal Reflection (TIR)
Conditions for TIR:
- Light must travel from denser to rarer medium
- Angle of incidence must exceed the critical angle
Critical angle: sin C = 1/n (where n = refractive index of denser medium w.r.t. rarer medium)
Applications: Optical fibres, mirage, brilliance of diamonds (C = 24.4° for diamond), totally reflecting prisms.
Optical Instruments
Simple microscope: Magnifying power = 1 + D/f (image at D) or D/f (image at infinity)
Where D = least distance of distinct vision = 25 cm.
Compound microscope:
- m = mₒ × mₑ
- At infinity: m = -(L/fₒ) × (D/fₑ)
Where L = tube length, fₒ = focal length of objective, fₑ = focal length of eyepiece.
Astronomical telescope:
- Normal adjustment (image at infinity): m = -fₒ/fₑ, Length = fₒ + fₑ
- Image at D: m = -(fₒ/fₑ)(1 + fₑ/D)
| Instrument | Magnifying Power (at ∞) | Tube Length |
|---|---|---|
| Simple microscope | D/f | — |
| Compound microscope | -(L/fₒ)(D/fₑ) | L + fₑ |
| Telescope | -fₒ/fₑ | fₒ + fₑ |
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Wave Optics: Key Concepts
Young's Double Slit Experiment (YDSE)
This is the most important derivation in Wave Optics. It proves the wave nature of light.
Path difference: Δx = yd/D
Where y = distance from central fringe, d = slit separation, D = screen distance.
For bright fringes (constructive): Δx = nλ → y = nλD/d
For dark fringes (destructive): Δx = (2n-1)λ/2 → y = (2n-1)λD/2d
Fringe width: β = λD/d
Key points:
- Fringe width is same for bright and dark fringes
- Central fringe is always bright
- If YDSE is done in a medium of refractive index n: β' = β/n (fringe width decreases)
- If one slit is covered → no interference pattern (just diffraction)
Single Slit Diffraction
Condition for minima: a sin θ = nλ (n = 1, 2, 3...)
Central maximum width: 2λD/a (twice the width of secondary maxima)
Secondary maxima at: a sin θ = (2n+1)λ/2
Where a = slit width.
Difference from interference:
- In diffraction, central maximum is the brightest and widest
- Intensity decreases sharply for higher-order maxima
Polarization
Malus's Law: I = I₀ cos²θ
Where I₀ = intensity of polarized light, θ = angle between pass axes of polarizer and analyser.
Brewster's Law: tan iB = n (refractive index)
At Brewster's angle, reflected light is completely polarized.
Key facts:
- Polarization proves light is a transverse wave
- Unpolarized light through a polaroid: intensity becomes I₀/2
- Two crossed polaroids: I = 0
Solved Examples
Example 1: Lens Combination
Q: Two thin lenses of focal lengths +20 cm and -40 cm are placed in contact. Find the power and focal length of the combination.
Solution:
- P₁ = 1/0.20 = +5 D
- P₂ = 1/(-0.40) = -2.5 D
- P = P₁ + P₂ = 5 + (-2.5) = +2.5 D
- f = 1/P = 1/2.5 = 0.4 m = 40 cm (converging)
Example 2: Prism — Minimum Deviation
Q: A prism of angle 60° produces minimum deviation of 30°. Find the refractive index.
Solution:
- n = sin[(A + δₘ)/2] / sin(A/2)
- n = sin[(60° + 30°)/2] / sin(60°/2)
- n = sin 45° / sin 30°
- n = (√2/2) / (1/2) = √2 ≈ 1.414
Example 3: Young's Double Slit Experiment
Q: In a YDSE, two slits are 0.5 mm apart and screen is 1 m away. Find the fringe width for light of wavelength 600 nm. Also find the position of the 3rd bright fringe.
Solution:
- d = 0.5 mm = 5 × 10⁻⁴ m, D = 1 m, λ = 600 nm = 6 × 10⁻⁷ m
- Fringe width β = λD/d = 6×10⁻⁷ × 1 / 5×10⁻⁴ = 1.2 × 10⁻³ m = 1.2 mm
- Position of 3rd bright fringe: y₃ = 3β = 3 × 1.2 = 3.6 mm from centre
Example 4: Malus's Law
Q: Unpolarized light of intensity I₀ passes through two polaroids whose pass axes make an angle of 60°. Find the final intensity.
Solution:
- After first polaroid: I₁ = I₀/2 (unpolarized becomes half)
- After second polaroid: I₂ = I₁ cos²60° = (I₀/2)(1/2)² = (I₀/2)(1/4) = I₀/8
Example 5: Critical Angle
Q: The refractive index of glass is 1.5. Find the critical angle for glass-air interface.
Solution:
- sin C = 1/n = 1/1.5 = 2/3
- C = sin⁻¹(2/3) ≈ 41.8°
Board Exam Important Questions
- Derive the expression for fringe width in Young's double slit experiment. (5 marks) — Almost guaranteed every year
- Derive the mirror formula for a concave mirror. (5 marks)
- Draw a ray diagram for compound microscope and derive the expression for its magnifying power. (5 marks)
- What is total internal reflection? State conditions and give two applications. (3 marks)
- Derive the lens maker's formula for a thin convex lens. (5 marks)
- Explain polarization. State and prove Malus's law. (3 marks)
- A convex lens of focal length 20 cm is placed coaxially with a convex mirror of radius 30 cm. The separation is 50 cm. Where should an object be placed to get its image on itself? (3 marks)
- In YDSE, what happens to fringe pattern if: (a) slit separation is increased (b) screen distance is decreased (c) experiment is performed in water. (3 marks)
Frequently Asked Questions
How many marks does Optics carry in the board exam?
The Optics unit (Ray + Wave) carries 14 marks out of 70 in the Physics theory paper. Ray Optics alone accounts for 8-9 marks and Wave Optics for 5-6 marks.
Which derivation from Optics is most important?
The YDSE fringe width derivation appears almost every year. The compound microscope and telescope magnifying power derivations are also frequently asked as 5-mark questions.
Is the prism formula important for boards?
Yes. The derivation of n = sin[(A+δₘ)/2]/sin(A/2) is a common 3-5 mark question. You should also know the i-δ graph and conditions for minimum deviation.
How do I remember the sign conventions?
Use the New Cartesian convention consistently. Draw the diagram first, mark the pole as origin, direction of light as +ve x-axis. Practice 10 problems — the signs become automatic.
What is the difference between interference and diffraction?
Interference happens when two separate wavefronts overlap (bright and dark fringes of equal width). Diffraction happens when light bends around a single obstacle or slit (central maximum is the widest and brightest, intensity drops off quickly).
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